71.4.1 problem 1

Internal problem ID [14373]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:28:04 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

dsolve(diff(y(x),x)=3*y(x)/( (x-5)*(x+3))+exp(-x),y(x), singsol=all)
 

\[ y = \frac {\left (\int \frac {{\mathrm e}^{-x} \left (x +3\right )^{{3}/{8}}}{\left (x -5\right )^{{3}/{8}}}d x +c_{1} \right ) \left (x -5\right )^{{3}/{8}}}{\left (x +3\right )^{{3}/{8}}} \]

✓ Solution by Mathematica

Time used: 0.104 (sec). Leaf size: 70

DSolve[D[y[x],x]==3*y[x]/( (x-5)*(x+3))+Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {3}{K[1]^2-2 K[1]-15}dK[1]\right ) \left (\int _1^x\exp \left (-K[2]-\int _1^{K[2]}\frac {3}{K[1]^2-2 K[1]-15}dK[1]\right )dK[2]+c_1\right ) \]